Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis | Zendy

P. D. Howell | Zendy; Jonathan J. Wylie | Zendy; Huaxiong Huang | Zendy; Robert M. Miura | Zendy

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Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis

Author(s) -

P. D. Howell,

Jonathan J. Wylie,

Huaxiong Huang,

Robert M. Miura

Publication year - 2007

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2007.7.553

Subject(s) - dimensionless quantity , thread (computing) , mechanics , axial symmetry , temperature gradient , thermodynamics , materials science , mathematics , physics , geometry , mechanical engineering , engineering , quantum mechanics

We consider the stretching of a thin cylindrical thread with viscosity that depends on temperature. The thread is pulled with a prescribed force while receiving continuous heating from an external axially nonuniform heater. We use the canonical equations derived by Huang et al. (2007) and consider the limit of large dimensionless heating rate. We show that the asymptotic solution depends only on the local properties of the heating near its maximal heating value. We derive a uniformly valid asymptotic solution for the shape and the temperature profiles during the stretching process. We use a criterion to determine when breaking will occur and derive simple analytical expressions for the shape at breaking that clearly show the influence of heating strength and the degree of localization of the heating. The asymptotic shape profiles give good agreement with numerical simulations. These results are applied to the formation of glass microelectrodes

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